Unsupervised word alignment is most often modeled as a Markov process that generates a sentence f conditioned on its translation e. A similar model generating e from f will make different alignment predictions.
Statistical machine translation systems combine the predictions of two directional models, typically using heuristic combination procedures like grow-diag-final. This paper presents a graphical model that embeds two directional aligners into a single model. Inference can be performed via dual decomposition, which reuses the efficient inference algorithms of the directional models. Our bidirectional model enforces a one-to-one phrase constraint while accounting for the uncertainty in the underlying directional models. The resulting alignments improve upon baseline combination heuristics in word-level and phrase-level evaluations.